U4 - indices and surds

a^m / aⁿ =

a^m-n

a^m x aⁿ =

a^m+n

(a^m)ⁿ =

a^mn

a⁰ =

1

a¹ =

a

a^-m =

1/a^m

a^1/m

^m√a

(a/b)^m =

a^m / b^m

how to solve algebraic indices questions

write both sides as a power of the same base number

√a x √b =

√ab

√a / √b =

√(a/b)

√a x √a =

a

how to rationalise the denominator if the denominator is a surd

multiply both sides of the fraction by the surd on the bottom

how to rationalise the denominator if the denominator is a surd + another number

use DOTS - multiply top and bottom by: first number of denominator -/+ second number - sign depends on which one is already there, opposites